Non-Bunch-Davies Initial State Reconciles Chaotic Models with BICEP and Planck

TL;DR

The paper tackles the tension between Planck data and BICEP2 results by relaxing the standard Bunch-Davies initial state for inflationary perturbations. It demonstrates that a non-Bunch-Davies initial state, parameterized by Bogoliubov coefficients, can modify the scalar and tensor power spectra through factors $\gamma_S$ and $\gamma_T$, shifting tilts and enabling either a blue tensor spectrum or a negative running of the scalar spectral index while maintaining Planck normalization and backreaction limits. The authors identify two viable routes: (i) introduce a scale-dependent tensor phase to realize a blue tensor tilt, and (ii) induce a negative running in $n_S$ via scale-dependent initial-state parameters, with the latter favored by data. This framework allows large-field chaotic models like $m^2\phi^2$ to be consistent with both Planck and BICEP2 when perturbations originate from a non-BD state with a high new-physics scale $M$, and it motivates the construction of explicit high-energy pre-inflationary models and potential observational tests in the two-point spectra.

Abstract

The BICEP2 experiment has announced a signal for primordial gravity waves with tensor-to-scalar ratio $r=0.2^{+0.07}_{-0.05}$ [arXiv:1403.3985]. There are two ways to reconcile this result with the latest Planck experiment [arXiv:1303.5082]. One is by assuming that there is a considerable tilt of $r$, $\mathcal{T}_r$, with a positive sign, $\mathcal{T}_r=d\ln r/d\ln k\gtrsim 0.57^{+0.29}_{-0.27}$ corresponding to a blue tilt for the tensor modes of order $n_T\simeq0.53 ^{+0.29}_{-0.27}$, assuming the Planck experiment best-fit value for tilt of scalar power spectrum $n_S$. The other possibility is to assume that there is a negative running in the scalar spectral index, $dn_S/d\ln k\simeq -0.02$ which pushes up the upper bound on $r$ from $0.11$ up to $0.26$ in the Planck analysis assuming the existence of a tensor spectrum. Simple slow-roll models fail to provide such large values for $\mathcal{T}_r$ or negative runnings in $n_S$ [arXiv:1403.3985]. In this note we show that a non-Bunch-Davies initial state for perturbations can provide a match between large field chaotic models (like $m^2φ^2$) with the latest Planck result [arXiv:1306.4914] and BICEP2 results by accommodating either the blue tilt of $r$ or the negative large running of $n_S$.